Consider the following three concentric systems: two thick shells and a solid sp
ID: 2122403 • Letter: C
Question
Consider the following three concentric systems: two thick shells and a solid
sphere (all conductors). The radii, in the increasing order, are a,b,c,d, and e. The small
sphere is given an excess charge of +2 C and the smaller shell is given an excess charge
of -4 C. The larger shell is electrically neutral. The system quickly comes to electrostatic
equilibrium state.
(a) What are the electric charges (values and signs) on the each of the 5 conducting
surfaces? Are these charges distributed uniformly? (Hint: induced charges)
(b) Use the concept of the Gauss%u2019s law to write down expressions (just formulas) for the
E-fields in all 6 regions (e.g. 0 < r < a, a < r < b , etc.). Make sure to write down the
enclosed charge for each region and also indicate the direction of the fields.
Explanation / Answer
a)
on a +2 C
on b -2 C
on c -2 C
on d +2 C
on e -2 C
b)
at 0<r<a E is radially outward
at a<r<b E is radially outward
at b<r<c E is zero
at c<r<d E is radially inward
at d<r<e E is zero
at r>e E is radially inward